That's generally how I run it IMTU.

Rather than overthrow a native potentate/heirarchy, the Empire/Emperor simply co-opts whatever power structure already exists, by granting Whoever is already in charge an Imperial title. While the Emperor prefers to made the Imperial title hereditary in the normal way - for better integration into the general Imperial culture - this isn't a hard and fast requirement. For example, on those member worlds which favor democratic rule, the Imperial title is simply added to those held by the highest local elected official. 

Of course - depending upon circumstances - the Empire may have had a hand in helping said Whoever INTO the position of being in charge just prior to the world "choosing" to join the Empire . . . but that's rarely acknowledged, at least not openly.